Boundaries permeability

At the initial stage of bulk copolymerization the reaction system represents the diluted solution of macromolecules in monomers. Every radical here is an individual microreactor with boundaries permeable to monomer molecules, whose concentrations in this microreactor are governed by the thermodynamic equilibrium whereas the polymer chain propagation is kinetically controlled. The evolution of the composition of a macroradical X under the increase of its length Z is described by the set of equations ... 

Polymers differ from other solids because they may absorb large amounts of solvents without dissolving. They also undergo large deformations when relatively small forces are involved. Swelling oeeurs in a heterogeneous two phase system a solvent surrounding a swollen body also called gel. Both phases are separated by the phase boundary permeable to... 

J. (1973) Chemical oscillations and multiple steady states due to variable boundary permeability. J. Theoret. Biol., 41, 503-521. 

The flowrate of oil into the wellbore is also influenced by the reservoir properties of permeability (k) and reservoir thickness (h), by the oil properties viscosity (p) and formation volume factor (BJ and by any change in the resistance to flow near the wellbore which is represented by the dimensionless term called skin (S). For semisteady state f/owbehaviour (when the effect of the producing well is seen at all boundaries of the reservoir) the radial inflow for oil into a vertical wellbore is represented by the equation ... 

Boundary layer effects Membranes (selective permeability for ions, gases etc.), ion exchangers, controlled release of pharmaceuticals. 

FIG. 2 The xy and a 3D projection of a typical osmotic MD simulation system. The semi-permeable membrane walls are in the yz plane. Periodic boundary conditions automatically generate an infinite pair of walls, infinite in the yz (transverse) directions, with alternating solution and solvent cells, each of thickness half the system width. 

The release of steroids such as progesterone from films of PCL and its copolymers with lactic acid has been shown to be rapid (Fig. 10) and to exhibit the expected (time)l/2 kinetics when corrected for the contribution of an aqueous boundary layer (68). The kinetics were consistent with phase separation of the steroid in the polymer and a Fickian diffusion process. The release rates, reflecting the permeability coefficient, depended on the method of film preparation and were greater with compression molded films than solution cast films. In vivo release rates from films implanted in rabbits was very rapid, being essentially identical to the rate of excretion of a bolus injection of progesterone, i. e., the rate of excretion rather than the rate of release from the polymer was rate determining. 

The evaluation of the apparent ionization constants (i) can indicate in partition experiments the extent to which a charged form of the drug partitions into the octanol or liposome bilayer domains, (ii) can indicate in solubility measurements, the presence of aggregates in saturated solutions and whether the aggregates are ionized or neutral and the extent to which salts of dmgs form, and (iii) can indicate in permeability measurements, whether the aqueous boundary layer adjacent to the membrane barrier, Umits the transport of drugs across artificial phospholipid membranes [parallel artificial membrane permeation assay (PAMPA)] or across monolayers of cultured cells [Caco-2, Madin-Darby canine kidney (MDCK), etc.]. 

Permeability-pH profiles, log Pe - pH curves in arhficial membrane models (log Pjpp - pH in cehular models), generally have sigmoidal shape, similar to that of log Dod - pH cf. Fig. 3.1). However, one feature is unique to permeabihty profiles the upper horizontal part of the sigmoidal curves may be verhcally depressed, due to the drug transport resistance arising from the aqueous boundary layer (ABL) adjacent to the two sides of the membrane barrier. Hence, the true membrane contribution to transport may be obscured when water is the rate-limiting resistance to transport. This is especially true if sparingly soluble molecules are considered and if the solutions on either or both sides of the membrane barrier are poorly stirred (often a problem with 96-well microhter plate formats). 

As discussed above, lipid membranes are dynamic structures with heterogeneous structure involving different lipid domains. The coexistence of different kinds of domains implies that boundaries must exist. The appearance of leaky interfacial regions, or defects, has been suggested to play a role in abrupt changes in solute permeabilities in the two-phase coexistence regions [91,92]. 

The physical process of melt ascent during two-phase flow models is typically based on the separation of melt and solid described by Darcy s Law modified for a buoyancy driving force. The melt velocity depends on the permeability and pressure gradients but the actual microscopic distribution of the melt (on grain boundaries or in veins) is left unspecified. The creation of disequilibria only requires movement of the fluid relative to the solid. 

They performed an extensive case study to demonstrate the use of automatic history matching to reservoir characterization. For example, if the estimated permeability of a particular zone is unrealistically small compared to geological information, there is a good chance that an impermeable barrier is present. Similarly if the estimated porosity of a zone approaches unrealistically high values, chances are the zone of the reservoir should be expanded beyond its current boundary. 

Specific situations are simulated by solving the set of system equations [i.e., Eqs. (4.1.1 and 4.1.2) or (4.1.3-4.1.6)] with pertinent boundary and initial conditions, fluid properties and macroscopic properties. Fluid properties are generally readily obtained. Consider now the media properties, specifically the porosity and permeability, which are required for simulating all flows through permeable media. 

The fluid properties and porosity and permeability are determined independently. Boundary and initial conditions are specified for the particular experiment to be considered. With specified multiphase flow functions, the state equations, Eqs. (4.1.28, 4.1.5 and 4.1.6), can be solved for the transient pressure and saturation distributions, p (z,t) and s,(z,t), t= 1, 2. The values for F can then be calculated, which correspond to the measured data Y. 

Karlsson, J. P. Artursson, P., A method for the determination of cellular permeability coefficients and aqueous boundary layer thickness in monolayers of intestinal epithelial (Caco-2) cells grown in permeable filter chambers, Int. J. Pharm. 7, 55-64 (1991). 

Boundary-layer separation and Reynolds flux. Kutateladze and Leont ev (1964, 1966) suggested that the flow boiling crisis can be analyzed using the concept of boundary-layer separation (blowoff) from a permeable flat plate with gas injection (without condensation), as shown in Figure 5.14. Kutateladze and Leont ev (1966) also give the critical condition of boundary layer separation from a flat plate with isothermal injection of the same fluid as... 

Figure 21 Linearized double reciprocal plot of the effective permeability coefficients and corresponding stirring rates to determine the power dependency of the stirring rate and mass transfer resistances for the aqueous boundary layers and the Caco-2 cell monolayer in the Transwell system. 

Table 12 Effective Permeability Coefficients and Thicknesses of the Aqueous Boundary Layer of the Caco-2 Cell Monolayer/ Transwell System as a Function of Stirring by Planar Rotating Shaker3...

Figure 31 Scheme for the protein-binding, diffusional, and partitioning processes and barriers that are encountered by a highly lipophilic and membrane-interactive drug (D) as it permeates through a cell within a continuous monolayer, h and h, thicknesses of the aqueous boundary layers. kd and ka, dissociation and association binding constants, respectively. P, protein molecule. Permeability coefficients Effective, Pe aqueous boundary layer, PABL and PW apical membrane, Pap basolateral membrane, Pbl. 

Figure 35 Relationship between the uptake permeability coefficient and the free drug concentration. PAEL is the permeability of the free drug across the aqueous boundary layer, and P BL is the same for the drug-albumin complex. [Redrawn from Raub et al. (1993) with permission from the publisher.]...

The identification and characterization of cell culture systems (e.g., Caco-2-cells) that mimic in vivo biological barriers (e.g., intestinal mucosa) have afforded pharmaceutical scientists the opportunity to rapidly and efficiently assess the permeability of drugs through these barriers in vitro. The results generated from these types of in vitro studies are generally expressed as effective permeability coefficients (Pe). If Pe is properly corrected to account for the barrier effects of the filter (PF) and the aqueous boundary layer (PAbl) as previously described in Section II.C, the results provide the permeability coefficient for the cell monolayer... 

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